Analytical Mechanics, 6 credits (TFYA40)
Analytisk mekanik, 6 hp
Main field of study
Mathematics Applied Mathematics Applied Physics PhysicsLevel
Second cycleCourse type
Programme courseExaminer
Iryna YakymenkoDirector of studies or equivalent
Magnus JohanssonAvailable for exchange students
YesMain field of study
Mathematics, Applied Mathematics, Applied Physics, PhysicsCourse level
Second cycleAdvancement level
A1XCourse offered for
- Physics and Nanoscience, Master's Programme
- Physics and Nanotechnology
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Materials Science and Nanotechnology, Master's programme
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Modern Physics, MechanicsIntended learning outcomes
The course represents the basic principles of classical mechanics within the framework of the variational approach. The knowledge of these principles is necessary for a deeper penetration into the structure of the classical mechanics itself, and also for a proper understanding of statistical mechanics, quantum mechanics etc. Furthermore, the methods of the analytical mechanics can serve as a set of the efficient tools for the solution of the majority of hard problems of mechanics and related topics.
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To achieve this aim students should be able to
- formulate the Lagrangian function for different mechanical systems,
- solve and analyze Lagrange's equations of motion for the set of generalized coordinates,
- formulate the Hamiltonian function for different mechanical systems,
- solve Hamiltion's equations of motion for the canonical variables,
- use the generating functions to make canonical transformations.
Course content
The variational approach to mechanics, Hamilton's principle, Lagrange's equations, first integrals and conservation theorems, elimination of cyclic variables, small oscillations theory, central force problem, Hamiltonian formulation of mechanics, canonical transformations, Hamilton-Jacobi theory,Poisson bracket formulation, introduction to analytical mechanics of continuous systems.
Teaching and working methods
Lectures and seminars with the solution of problems
Examination
TEN1 | Written Examination | U, 3, 4, 5 | 6 credits |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Quantum Mechanics can be followed in parallel, Quantum Dynamic
Department
Institutionen för fysik, kemi och biologiDirector of Studies or equivalent
Magnus JohanssonExaminer
Iryna YakymenkoCourse website and other links
http://www.ifm.liu.se/undergrad/fysikgtu/coursepage.html?selection=all&sort=kkEducation components
Preliminary scheduled hours: 56 hRecommended self-study hours: 104 h
Course literature
Additional literature
Books
H. Goldstein, Ch. Poole, J. Safko, (2001) Classical Mechanics 3(selected parts). Addison & Wesley
Compendiums
I.I. Yakymenko, Lecture Notes in Analytical MechanicsI.I. Yakymenko, Set of Problems in Analytical MechanicsAdditional literature
Books
(selected parts). Addison & Wesley
Compendia
TEN1 | Written Examination | U, 3, 4, 5 | 6 credits |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
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